Heart disease is the number one killer in the United States. Heart attacks kill nearly a million Americans a year—rich and poor, the famous and the forgotten. In fact, cardiovascular disease is so common that 64 million Americans suffer from some form of it (and 39 million of these people are age 65 years old or younger). Right ventricular (RV) dysfunction is one of the more common causes of heart failure in patients with congenital heart defects and often leads to impaired functional capacity and premature death. Patients with repaired Tetralogy of Fallot (ToF), a congenital heart defect which includes a ventricular septal defect and severe RV outflow obstruction, account for the majority of cases with late onset RV failure. The mechanism of failure is a complex interaction of chronic pulmonary valve regurgitation (present since the original repair), a non-contractile and sometimes aneurysmal RV outflow, ventricular scarring from the incision to remove RV outflow muscle at the original repair, and some residual obstruction to RV outflow. It is believed that mechanical factors play an important role in the development of the disease leading to RV failure.
Image-based computational modeling and medical imaging technologies have made considerable advances in biological and clinical research in recent years (Axel, L., 2002, “Biomechanical Dynamics of the Heart With MRI,” Annu. Rev. Biomed. Eng., 4, pp. 321-347; Bloomgarden, D. C., Fayad, Z. A., Ferrari, V. A., Chin, B., Sutton, M. G., and Axel, L., 1997, “Global Cardiac Function Using Fast Breath-Hold MRI: Validation of New Acquisition and Analysis Techniques,” Magn. Reson. Med., 37, pp. 683-692; Geva, T., Greil, G. F., Marshall, A. C., Landzberg, M., and Powell, A. J., 2002, “Gadolinium-Enhanced 3-Dimensional Magnetic Resonance Angiography of Pulmonary Blood Supply in Patients With Complex Pulmonary Stenosis or Atresia: Comparison With X-Ray Angiography,” Circulation, 106, pp. 473-478; Geva, T., Powell, A. J., Crawford, E. C., Chung, T., and Colan, S. D., 1998, “Evaluation of Regional Differences in Right Ventricular Systolic Function by Acoustic Quantification Echocardiography and Cine Magnetic Resonance Imaging,” Circulation, 98, pp. 339-345; Geva, T., Sandweiss, B. M., Gauvreau, K., Lock, J. E., and Powell, A. J., 2004, “Factors Associated With Impaired Clinical Status in Long-Term Survivors of Tetralogy of Fallot Repair Evaluated by Magnetic Resonance Imaging,” J. Am. Coll. Cardiol., 43, pp. 1068-1074; Guccione, J. M., K. D. Costa, A. D. McCulloch, (1995) J. Biomech. 28(10), 1167-77; Guccione, J. M., A. D. McCulloch, L. K. Waldman, (1991) J Biomech Eng. 113(1), 42-55; Guccione, J. M., G. S. Le Prell, P. P. de Tombe, W. C. Hunter, (1997) J. Biomech. 30(2), 189-192; Guccione, J. M., A. D. McCulloch, (1993) J Biomech Eng. 115(1), 72-81; Guccione, J. M., L. K. Waldman, A. D. McCulloch, (1993) J Biomech Eng. 115(1), 82-90; Holzapfel, G. A., T. C. Gasser, R. W. Ogden, (2000) Journal of Elasticity, 61, 1-48; Holzapfel G. A., M. Stadler, C. A. J. Schulze-Bause, (2002) Annals of Biomedical Engineering, 30(6), 753-767; J. D. Humphrey, Cardiovascular Solid Mechanics, Springer-Verlag, New York, 2002; P. J. Hunter, A. J. Pullan, B. H. Smaill, “Modeling total heart function,” Annu Rev Biomed Eng., 5:147-177, 2003; Kuehne, T., Yilmaz, S., Steendijk, P., Moore, P., Groenink, M., Saaed, M., Weber, O., Higgins, C. B., Ewert, P., Fleck, E., Nagel, E., Schulze-Neick, I., and Lange, P., 2004, “Magnetic Resonance Imaging Analysis of Right Ventricular Pressure-Volume Loops In Vivo Validation and Clinical Application in Patients With Pulmonary Hypertension,” Circulation, 110, pp. 2010-2016; McCulloch, A. M. et al., (2007) Continuity 6 (a package distributed free by the National Biomedical Computation Resource); McCulloch, A. M., L. Waldman, J. Rogers, J. Guccione, (1992) Critical Rev. in Biomedical Engineering, 20(5,6): 427-449; M. P. Nash, P. J. Hunter, “Computational Mechanics of the Heart, From Tissue Structure to Ventricular Function,” Journal of Elasticity, 61:113-141, 2000; C. S. Peskin, Mathematical Aspects of Heart Physiology, Lecture Notes of Courant Institute of Mathematical Sciences, New York, 1975; Peskin, C. S., D. M. McQueen, (1992) Crit Rev Biomed Eng. 20(5-6), 451-459; J. M. Rogers and A. D. McCulloch, “Nonuniform muscle fiber orientation causes spiral wave drift in a finite element model of cardiac action potential propagation,” J Cardiovasc Electrophysiol. 5(6):496-509, 1994; N. R. Saber, A. D. Gosman, N. B. Wood, P. J. Kilner, C. L. Charrier, and D. N. Firman, “Computational flow modeling of the left ventricle based on in vivo MRI data: initial experience,” Annals of Biomech. Engng., 29:275-283, 2001; M. S. Sacks and C. J. Chuong, “Biaxial mechanical properties of passive right ventricular free wall myocardium,” J Biomech Eng, 115:202-205, 1993; C. Stevens and P. J. Hunter, “Sarcomere length changes in a 3D mathematical model of the pig ventricles,” Progress in Biophysics & Molecular Biology, 82:229-241, 2003; C. Stevens, E. Remme, I. LeGrice, P. J. Hunter, “Ventricular mechanics in diastole: material parameter sensitivity,” J Biomech., 36(5):737-48, 2003; D. Tang, C. Yang, J. Zheng, P. K. Woodard, G. A. Sicard, J. E. Saffitz, and C. Yuan, “3D MRI-Based Multi-Component FSI Models for Atherosclerotic Plaques a 3-D FSI model,” Annals of Biomedical Engineering, 32(7):947-960, 2004; Tang D, Yang C, Zheng J, Woodard P K, Saffitz J E, Petruccelli J D, Sicard G A, Yuan C. “Local maximal stress hypothesis and computational plaque vulnerability index for atherosclerotic plaque assessment.” Ann Biomed Eng 2005; 33(12):1789-1801; T. P. Usyk, A. D. McCulloch, “Relationship between regional shortening and asynchronous electrical activation in a three-dimensional model of ventricular electromechanics,” J Cardiovasc Electrophysiol., 14(10 Suppl):S196-202, 2003; F. J. Vetter and A. D. McCulloch, “Three-dimensional stress and strain in passive rabbit left ventricle: a model study,” Annals of Biomech. Engng. 28:781-792, 2000; Vliegen, H. W., Van Straten, A., De Roos, A., Roest, A. A., Schoof, P. H., Zwinderman, A. H., Ottenkamp, J., Van Der Wall, E. E., and Hazekamp, M. G., 2002, “Magnetic Resonance Imaging to Assess the Hemodynamic Effects of Pulmonary Valve Replacement in Adults Late After Repair of Tetralogy of Fallot,” Circulation, 106, pp. 1703-1707). Use of computer-assisted procedures is becoming more and more popular in clinical decision making processes and computer-aided surgeries. Early three-dimensional (3D) models for blood flow in the heart include Peskin's model which introduced fiber-based left ventricle (LV) model and the celebrated immersed-boundary method to study blood flow features in an idealized geometry with fluid-structure interactions (FSIs; Peskin, 1975, see above). A large amount of effort has been devoted to quantifying heart tissue mechanical properties and fiber orientations mostly using animal models (K. D. Costa, Y. Takayama, A. D. McCulloch, J. W. Covell, “Laminar fiber architecture and three-dimensional systolic mechanics in canine ventricular myocardium,” Am J. Physiol. 276(2 Pt 2):H595-607, 1999; Nash and Hunter, 2000, see above; Rogers and McCulloh, 1994, see above; Sacks and Chuong, 1993, see above; Y. Takayama, K. D. Costa, J. W. Covell, “Contribution of laminar myofiber architecture to load-dependent changes in mechanics of LV myocardium,” Am J Physiol Heart Circ Physiol. 282(4):H1510-20, 2002). Humphrey's book provides a comprehensive review of the literature (Humphrey, 2002, see above).
More recent efforts include introduction of magnetic resonance image (MRI)-based fluid-only or structure-only 3D models to investigate flow and stress/strain behaviors in the whole ventricle (either RV or LV) (Guccione, Costa and McCulloch, 1995, see above; Guccione, McCulloch and Waldman, 1991, see above; Guccione et al., 1997, see above; Guccione and McCulloch, 1993, see above; Guccione, Waldman and McCulloch, 1993, see above; K. May-Newman and A. D. McCulloch, “Homogenization modeling for the mechanics of perfused myocardium,” Prog Biophys Mol Biol. 69(2-3):463-81, 1998; McCulloch et al., 2007, see above; McCulloch et al., 1992, see above; Nash and Hunter, 2000, see above; Saber et al., 2001, see above; Sacks and Chuong, 1993, see above; Stevens and Hunter, 2003, see above; Stevens et al., 2003, see above; Usyk and McCulloch, 2003, see above; Tang et al., 2004, see above; F. J. Vetter and A. D. McCulloch, “Three-dimensional analysis of regional cardiac function: a model of rabbit ventricular anatomy,” Prog Biophys Mol Biol. 69(2-3):157-183, 1998; Vetter and McCulloch, 2000, see above).
Stevens et al. introduced a 3D finite element (FE) solid model of the heart based on measurements of the geometry and the fiber and sheet orientations of pig hearts. The end-diastolic deformation of the model was computed using the “pole-zero” constitutive law to model the mechanics of passive myocardial tissue specimens. The sensitivities of end-diastolic fiber-sheet material strains and heart shape to changes in the material parameters were investigated (Stevens and Hunter, 2003, see above; Stevens et al., 2003, see above).
McCulloch et al. performed extensive research for 3D ventricular geometry and myofiber architecture of the rabbit heart. Their work and their Continuity package included experimental and modeling studies of 3D cardiac mechanics and electrophysiology (May-Newmand and McCulloch, 1998, see above; McCulloch et al., 2007, see above; McCulloch, Waldman and Guccione, 1992, see above; Usyk and McCulloch, 2003, see above; T. P. Usyk and R. Kerckhoffs, “Three dimensional electromechanical model of porcine heart with penetrating wound injury,” Stud Health Technol Inform., 111:568-573, 2005; Vetter and McCulloch, 1998, see above; Vetter and McCulloch, 2000, see above).
In a series of papers, Guccione et al. introduced anisotropic passive and active ventricle models where an additional tension term was added to the stress field to model active heart contractions RV (Guccione, Costa and McCulloch, 1995, see above; Guccione, McCulloch and Waldman, 1991, see above; Guccione et al., 1997, see above; Guccione and McCulloch, 1993, see above; Guccione, Waldman and McCulloch, 1993, see above).
The papers by Nash and Hunter (see above) and Hunter, Pullan and Smaill (see above) provided comprehensive reviews for heart modeling, including tissue properties, fiber orientation, passive and active mechanical models, electromechanical models, and whole heart models. Those animal models provide some insight for human heart mechanics and function with a huge effort and great detail.